title: A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media.
abstract: The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature.
authors.affiliation: College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China.
authors.forename: Hongguang
authors.initials: H
authors.lastname: Sun
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: Yong
authors.initials: Y
authors.lastname: Zhang
authors.forename: Jianting
authors.initials: J
authors.lastname: Zhu
authors.forename: Wen
authors.initials: W
authors.lastname: Chen
keywords: Fractal model; Non-Boltzman scaling; Richards equation; Water content